A301791 -id:A301791 - cp's OEIS frontend

A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 16, 34, 16, 13, 14, 25, 40, 89, 32, 21, 22, 41, 64, 100, 233, 64, 34, 35, 74, 111, 169, 252, 610, 128, 55, 56, 132, 219, 311, 441, 632, 1597, 256, 89, 90, 239, 443, 749, 874, 1156, 1588, 4181, 512, 144, 145, 437, 904, 1803, 2544, 2454

Offset: 1

R. H. Hardin, Mar 29 2018

Table starts
...1....2....3....5.....8.....13.....21......34.......55........89.......144
...2....5....6....9....14.....22.....35......56.......90.......145.......234
...4...13...16...25....41.....74....132.....239......437.......800......1468
...8...34...40...64...111....219....443.....904.....1860......3856......8015
..16...89..100..169...311....749...1803....4257....10353.....25491.....62623
..32..233..252..441...874...2544...7795...22456....66659....203926....621905
..64..610..632.1156..2454...8705..33860..120603...444357...1715911...6574776
.128.1597.1588.3025..6906..29750.148299..655332..3014296..14863160..72345489
.256.4181.3988.7921.19427.101869.646838.3557239.20467528.129324707.802690313

			Some solutions for n=5 k=4
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0. .0..0..1..0
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .1..1..1..0
..0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..1. .1..0..1..0
..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..880

Column 1 is A000079(n-1).
Column 2 is A001519(n+1).
Row 1 is A000045(n+1).
Row 2 is A301791.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = a(n-1) +3*a(n-2) +2*a(n-3)
k=4: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3) for n>4
k=5: a(n) = 2*a(n-1) +3*a(n-2) -a(n-3) -2*a(n-4) -3*a(n-5) +2*a(n-6) for n>8
k=6: [order 11] for n>12
k=7: [order 14] for n>17
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-3) for n>5
n=3: a(n) = 2*a(n-1) -a(n-4) for n>6
n=4: a(n) = 2*a(n-1) +a(n-3) -a(n-4) -2*a(n-6) +a(n-7) for n>9
n=5: [order 14] for n>17
n=6: [order 27] for n>32
n=7: [order 47] for n>52

cp's OEIS Frontend

A301964 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.

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